Socioeconomic Determinants of Fertility Behavior in Developing Nations Theory and Initial Results (1982) / Chapter Skim
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1.4 Reduced and Semireduced Form Implications of the Model
1.4 Reduced and Semireduced Form Implications of the Model
Pages 31-44
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From page 31... ...
This leads to development of implied and actual semireduced form equations for these variables, followed by a discussion of inferences that can be drawn about the coefficient signs in these equations. The Need for Reduction As shown above, the threefold distinction between onset, early fertility, and later fertility permits development of an intricate and comprehensive micro model embodying a number of untested hypotheses.
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From page 32... ...
from various ideal-typic anchor points of the traditional/transitional continuum. Because the model postulates contextual variability in a large proportion of the micro structural coefficients, its testing must involve estimation of its micro and macro components.
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From page 33... ...
The following subsection formulates a model for examining hypotheses about the relationships between socioeconomic position and CEB, CM, and LCU. Implied and Actual semireduced Form Equations To study the implications of the micro model for the relationships between socioeconomic position and CEB, CM, and LCU, we obtain actual and implied semireduced form equations from the structural equations by a process of substitution to remove endogenous variables from the lists of predictors.
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From page 34... ...
19) , the actual and implied semireduced form effects of RESC, WED, WBM, and HOCC cannot be read directly from the equations.
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From page 35... ...
First, the child mortality equation should be a linear and additive function of the designated socioeconomic variables. In the modeling of child mortality as a function of designated socioeconomic variables, replicated demonstration of nonlinearities (in the sense of sign reversals over the range of a predetermined variable)
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From page 36... ...
In addition, derivation of coefficient signs in the implied and actual semireduced form equations requires assumptions about the intercepts for structural equations (~.1)
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From page 37... ...
Originally, we expected positive boy and girl sufficiency effects on child mortality. However, there are routes by which the opposite conclusion can be reached.
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From page 38... ...
All of our conclusions about the implied and actual semireduced form effects of the socioeconomic variables on child mortality, contraceptive use, and children ever born are summarized in Table 1.3. The remaining discussion in this section explains how the conclusions reported in Table 1.3 have been reached.
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From page 39... ...
Effects which are necessarily zero because the variables are undefined for a particular setting are indicated by an axe. Alternative assumptions about the effects of sex preference are labeled as follows: CM a.
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From page 40... ...
It results from structuring the model to include intermediate outcomes, and probably could not be reached otherwise. The implied semireduced form coeff icients for child mortality in transitional settings share certain similarities with those for traditional settings.
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From page 41... ...
Without prior knowledge, it is uncertain whether the semireduced form effects of RESC, WED, and WBM are positive, zero, or negative in transitional settings. To summarize the implied semireduced form effects of the socioeconomic variables on child mortality in traditional and transitional contexts, out of twelve coefficients, seven have implied signs, two are indeterminate as to sign regardless of sex sufficiency effects, and three are determinate given prior knowledge of particular forms of those effects.
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From page 42... ...
me three scenarios that lead to the conclusions summarized in Table 1.3, Part A are as follows: sex composition is a matter of indifference; boy and girl sufficiency have positive additive effects on LCU and negative additive effects on LF; and the interaction of SCB and SES enhances LCU and reduces LF. Considering first those variables which do not interact in the semireduced form equation, the semireduced form effects of RES, WSM, and HED are unambiguously positive in transitional settings under these three sets of assumptions.
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From page 43... ...
This equation is thus additive, with all of its effects implied to be positive, if present. The implied semireduced form equation for CEB in transitional settings contains interactions and nonlinearities, as shown above.
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From page 44... ...
On the other hand, if we think alternative assumptions about sex preference are appropriate, we can reach conclusions of varying firmness about the socioeconomic effects. ffl ese conclusions concern functional form, as well as expectations about the nature of covariabilty between implied and actual semireduced form socioeconomic effects and the degree of transitionality.
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